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Duality on Optimization and Control Theories

Research Project

Project/Area Number 17H01700
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Mathematical informatics
Research InstitutionKyushu University

Principal Investigator

Waki Hayato  九州大学, マス・フォア・インダストリ研究所, 准教授 (00567597)

Co-Investigator(Kenkyū-buntansha) 蛯原 義雄  九州大学, システム情報科学研究院, 教授 (80346080)
瀬部 昇  九州工業大学, 大学院情報工学研究院, 教授 (90216549)
Project Period (FY) 2017-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥6,630,000 (Direct Cost: ¥5,100,000、Indirect Cost: ¥1,530,000)
Fiscal Year 2019: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2018: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2017: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Keywords最適化理論 / 制御理論 / 行列不等式 / 面的縮小法 / 双対性 / H∞制御
Outline of Final Research Achievements

We considered the ill-posedness in linear matrix inequality (LMI) for H-infinity control problem. For this, we applied facial redution and revealed the relationship between the strict feasibility of the dual and invariant zeros in the linear time-invariant dynamical system. Furthermore, the positive definiteness in an optimal solution of the LMI is requreid for desired H-infinity control. We obtained a necessary condition to be positive definite for an optimal soluiton.

Academic Significance and Societal Importance of the Research Achievements

最適化理論の技術を制御理論の分野に用いたという点で, 異分野融合型の研究を実施したといえよう. 最小解が存在しない不良設定な最適化問題は, 「poor modeling」によるものと捉えがちだが, 双対問題まで考慮して凸計画問題を構成しなければならない, というのはモデリングの観点から大変難しい作業である. 本研究では, 対象とする動的システムの不変零点で, ある程度対応できることを示唆している.

Report

(4 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • Research Products

    (16 results)

All 2019 2018 2017

All Journal Article (6 results) (of which Peer Reviewed: 5 results) Presentation (10 results) (of which Int'l Joint Research: 4 results,  Invited: 2 results)

  • [Journal Article] Positive Definiteness in Linear Matrix Inequality Problem for H-infinity Output Feedback Control Problem2019

    • Author(s)
      Waki Hayato
    • Journal Title

      IEEE Control Systems Letters

      Volume: 3 Issue: 2 Pages: 446-451

    • DOI

      10.1109/lcsys.2019.2898385

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Reduction of H∞ state feedback control problems for the MIMO servo systems2018

    • Author(s)
      Waki Hayato、Sebe Noboru
    • Journal Title

      Asian Journal of Control

      Volume: - Issue: 3 Pages: 1025-1037

    • DOI

      10.1002/asjc.1985

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Strong feasibility of the dual problem of linear matrix inequality for H-infinity output feedback control problem2018

    • Author(s)
      Hayato Waki, Noboru Sebe
    • Journal Title

      Proceedings of SICE International Symposium on Control Systems 2018

      Volume: - Pages: 47-53

    • DOI

      10.23919/siceiscs.2018.8330155

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Application of Facial Reduction to H∞ State Feedback Control Problem2018

    • Author(s)
      Hayato Waki, Noboru Sebe
    • Journal Title

      International Journal of Control

      Volume: - Issue: 2 Pages: 47-53

    • DOI

      10.1080/00207179.2017.1351625

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Reduction of H-infinity state feedback control problems for the servo systems2017

    • Author(s)
      Hayato Waki, Noboru Sebe
    • Journal Title

      Proceedings of 2017 11th Asian Control Conference (ASCC),

      Volume: - Pages: 2244-2249

    • DOI

      10.1109/ascc.2017.8287524

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dominant Pole Analysis of Neutral-Type Time Delay Positive Systems2017

    • Author(s)
      Yosio Ebihara
    • Journal Title

      Proceedings of the 55th IEEE Conference on Decision and Control

      Volume: - Pages: 6555-6560

    • DOI

      10.1109/cdc.2017.8264647

    • Related Report
      2017 Annual Research Report
  • [Presentation] L1-induced norm analysis of positive systems and its application2019

    • Author(s)
      Yoshio Ebihara
    • Organizer
      Kolloquium Technische Kybernetik
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] H∞フィードバック制御問題の正定値解について2019

    • Author(s)
      脇 隼人
    • Organizer
      第6回 制御部門マルチシンポジウム
    • Related Report
      2018 Annual Research Report
  • [Presentation] Facial reduction for H-infinity state feedback control2018

    • Author(s)
      Hayato Waki
    • Organizer
      International Workshop on "Control and Optimization"
    • Related Report
      2018 Annual Research Report
  • [Presentation] H-infinity制御に対する面的縮小法2018

    • Author(s)
      脇 隼人
    • Organizer
      科学研究費 基盤研究(A)「新時代の最適化モデルに基づく意思決定支援プラットフォームの研究と開発」による2018年度ワークショップ
    • Related Report
      2018 Annual Research Report
  • [Presentation] LTI System Analysis via Conversion to Externally Positive Systems: Order Reduction via Elimination and Duplication Matrices2018

    • Author(s)
      Yoshio Ebihara
    • Organizer
      23rd International Symposium on Mathematical Theory of Networks and Systems
    • Related Report
      2018 Annual Research Report
  • [Presentation] Strong feasibility of the dual problem of linear matrix inequality for H-infinity output feedback control problem2018

    • Author(s)
      Hayato Waki
    • Organizer
      SICE International Symposium on Control Systems 2018
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Reduction of H-infinity state feedback control problems for the servo systems2017

    • Author(s)
      Noboru Sebe
    • Organizer
      11th Asian Control Conference (ASCC)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] H∞制御に対する面的縮小法2017

    • Author(s)
      脇 隼人
    • Organizer
      第60回自動制御連合講演会
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Dominant Pole Analysis of Neutral-Type Time Delay Positive Systems2017

    • Author(s)
      Yoshi Ebihara
    • Organizer
      55th IEEE Conference on Decision and Control
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Reduction of SDPs in H-infinity Control of SISO Systems and Performance Limitations Analysis2017

    • Author(s)
      Yoshi Ebihara
    • Organizer
      The IFAC Workshop ``Robert Tempo'' on Uncertain Dynamical Systems (WUDS)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research

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Published: 2017-04-28   Modified: 2021-02-19  

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